class Solution {
public:
    int minDistance(string word1, string word2) {
        int m = word1.size(), n = word2.size();
        vector<vector<int>> dp(m + 1, vector<int> (n + 1, 0));
        for(int i = 1; i <= m; ++i)
            dp[i][0] = i;
        for(int i = 1; i <= n; ++i)
            dp[0][i] = i;
        
        for(int i = 1; i <= m; ++i)
        {
            for(int j = 1; j <= n; ++j)
            {
                int a = dp[i - 1][j] + 1;
                int b = dp[i][j - 1] + 1;
                int c = dp[i - 1][j - 1];
                if(word1[i - 1] != word2[j - 1]) ++c;
                dp[i][j] = min({ a, b, c });
            }
        }
        return dp[m][n];
    }
};
